As modern abstract algebra was developed in the 50's and 60's, it was fruitfully turned towards this path with the creation of the theory of finite automata. The first fundamental result in this development was Kleene's Theorem demonstrating that the class of recognizable languages is the class of rational languages [1]}. In 1956, Schützenberger defined the syntactic monoid, a canonical monoid attached to each language [2]}. Later, he proved that a language is star-free exactly when its syntactic monoid is finite and aperiodic [3]}. At this point mathematicians started to consider the algebraic geometry of these monoids as Birkhoff [4]} and latter Eilenberg [5]} and Reiterman [6]} developed wrote about varieties of these monoids (infinite and finite respectively). Thus we have a well established and important connection between theoretical computer science and pure algebraic geometry.
